import Mathlib.Tactic /-! # USA Mathematical Olympiad 1982, Problem 4 Prove that there exists a positive integer k such that k⬝2ⁿ + 1 is composite for every integer n. -/ namespace Usa1982P4 theorem usa1982_p4 : ∃ k : ℕ, 0 < k ∧ ∀ n : ℕ, ¬ Prime (k * (2 ^ n) + 1) := sorry

This problem does not yet have a complete solution.